Subgroups — #564×Dic₅₉ #28751411

Order 15104.

1800 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21427282	C₂	1	15	yes	maximal
2	#125×Dic₅₉	C₂	1	15	yes	maximal
3	C₂×C₅₉×#564	C₂	1	1	yes	maximal, characteristic
4	#16837301	C₂²	1	30	yes	—
5	#16837288	C₂²	1	60	yes	—
6	#16837268	C₂²	1	15	yes	—
7	C₄⋊C₄×Dic₅₉	C₂²	1	30	yes	—
8	C₄²×Dic₅₉	C₂²	1	5	yes	—
9	C₅₉×#564	C₄	1	16	yes	complemented
10	C₂×#125×C₅₉	C₂²	1	15	yes	—
11	C₂×C₄⋊Dic₅₉	C₂³	1	30	yes	—
12	C₂×C₄×Dic₅₉	C₂³	1	15	yes	—
13	C₂×C₄×Dic₅₉	C₂³	1	15	yes	—
14	C₅₉⋊#95	C₂³	1	60	yes	—
15	#125×C₅₉	C₂×C₄	1	120	yes	—
16	C₂×C₄⋊C₄×C₅₉	C₂³	1	30	yes	—
17	C₂×C₄²×C₅₉	C₂³	1	5	yes	—
18	C₂²×C₄×C₅₉	C₂⁴	1	15	yes	—
19	C₂²×Dic₅₉	C₂⁴	1	15	yes	—
20	C₂²×Dic₅₉	C₂⁴	1	1	yes	characteristic
21	C₄⋊C₄×C₅₉	C₂²×C₄	1	120	yes	—
22	C₄²×C₅₉	C₂²×C₄	1	20	yes	—
23	C₄⋊Dic₅₉	—	4	30	no	—
24	C₄×Dic₅₉	—	2	30	no	—
25	C₄×Dic₅₉	—	4	15	no	—
26	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
27	C₂×C₄×C₅₉	—	2	15	no	—
28	C₂×C₄×C₅₉	—	2	15	no	—
29	C₂×C₄×C₅₉	C₂³×C₄	1	30	yes	—
30	C₂×Dic₅₉	—	2	15	no	—
31	C₂×Dic₅₉	—	2	30	no	—
32	C₂×Dic₅₉	2₋¹⁺⁴	1	6	yes	—
33	C₄×#564	—	59	1	no	maximal, Sylow
34	C₂²×C₅₉	C₂⁴×C₄	1	1	yes	characteristic
35	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	3	yes	—
36	C₂²×C₅₉	#585	1	3	yes	—
37	C₄×C₅₉	—	2	30	no	—
38	Dic₅₉	—	4	15	no	—
39	Dic₅₉	#564	1	4	yes	direct product factor
40	C₂×#564	D₅₉	1	1	yes	characteristic
41	#2382	—	59	15	no	—
42	C₄×#125	—	59	15	no	—
43	C₂×C₅₉	C₄×2₋¹⁺⁴	1	3	yes	—
44	C₂×C₅₉	C₂×#564	1	1	yes	characteristic
45	C₂×C₅₉	#3531	1	3	yes	—
46	#564	Dic₅₉	1	16	yes	direct product factor
47	C₂×#125	C₂×D₅₉	1	15	yes	—
48	#389	—	59	30	no	—
49	#387	—	59	60	no	—
50	#382	—	59	15	no	—
51	C₄×C₄⋊C₄	—	59	30	no	—
52	C₄³	—	59	5	no	—
53	C₅₉	C₄×#564	1	1	yes	characteristic, complemented, Sylow
54	#125	C₂×Dic₅₉	1	120	yes	—
55	C₂×C₄⋊C₄	—	59	30	no	—
56	C₂×C₄⋊C₄	C₂²×D₅₉	1	30	yes	—
57	C₂×C₄²	—	59	15	no	—
58	C₂×C₄²	—	59	15	no	—
59	C₂×C₄²	C₂²×D₅₉	1	5	yes	—
60	#95	—	59	60	no	—
61	C₂²×C₄	—	59	1	no	—
62	C₂²×C₄	—	59	15	no	—
63	C₂²×C₄	C₂³×D₅₉	1	15	yes	—
64	C₄⋊C₄	—	236	30	no	—
65	C₄⋊C₄	C₂²×Dic₅₉	1	120	yes	—
66	C₄²	—	118	30	no	—
67	C₄²	—	236	15	no	—
68	C₄²	C₂²×Dic₅₉	1	20	yes	—
69	C₂³	C₂⁴×D₅₉	1	1	yes	characteristic
70	C₂×C₄	—	2	15	no	—
71	C₂×C₄	—	2	15	no	—
72	C₂×C₄	—	59	6	no	—
73	C₂×C₄	—	118	15	no	—
74	C₂×C₄	—	118	30	no	—
75	C₂×C₄	C₂³×Dic₅₉	1	30	yes	—
76	C₂²	C₂⁴×Dic₅₉	1	1	yes	characteristic
77	C₂²	2₋¹⁺⁴×D₅₉	1	3	yes	—
78	C₂²	#16838239	1	3	yes	—
79	C₄	—	2	30	no	—
80	C₄	—	59	4	no	—
81	C₄	—	236	15	no	—
82	C₂	2₋¹⁺⁴×Dic₅₉	1	3	yes	—
83	C₂	#564×D₅₉	1	1	yes	characteristic
84	C₂	#21438244	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₉
commutator	C₂²×C₅₉	C₂⁴×C₄
Fitting	C₂×C₅₉×#564	C₂
socle, prime radical, cosocle	C₂³×C₅₉	C₂⁵
hypercenter	C₂×#564	D₅₉
hypocenter	C₅₉	C₄×#564
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ C₂×#564

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
9. C₅₉×#564	C₄	semidirect
39. Dic₅₉	#564	direct (N × H)
46. #564	Dic₅₉	direct (N × H)
53. C₅₉	C₄×#564	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#21427282	2
#125×Dic₅₉	2
C₂×C₅₉×#564	2
C₄×#564	59

Subgroups — #564×Dic59 #28751411

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #564×Dic₅₉ #28751411